# Phase 8 Part A: Housing ΔRHPI Fix

## Before Fix (pct_change × 100)

- N = 1927
- Mean = 54.99, Std = 3044.39
- Min = -52921.41, Max = 109893.90
- p1 = -1688.08, p99 = 1953.02
- Negative HPI values: 493 (24.9%)

## After Fix (log-difference × 100)

- N = 1255
- Mean = 5.03, Std = 109.50
- Min = -583.55, Max = 700.30
- p1 = -314.69, p99 = 315.22

## Re-run Housing Regressions (Corrected d_rhpi)

| Model | N | Countries | R² | Key Variables |
|---|---|---|---|---|
| M1: Z → Δreal HPI | 541 | 23 | 0.068 | Z_1=647.36* (p=0.080) |
| M2: age ratios → Δreal HPI | 541 | 23 | 0.063 | old_dep=78.07 (p=0.390); youth_dep=63.06 (p=0.535) |
| M3: Z×KAOPEN → Δreal HPI | 541 | 23 | 0.068 | Z_1=70.88 (p=0.960) |
| M4: CA/GDP → Δreal HPI | 541 | 23 | 0.063 | ca_gdp=0.21 (p=0.803) |
| M5: OECD Z → Δreal HPI | 541 | 23 | 0.068 | Z_1=647.36* (p=0.080) |
| M6: Z + LE² → Δreal HPI | 541 | 23 | 0.071 | Z_1=627.16* (p=0.098) |
| M7: post-GFC Z → Δreal HPI | 219 | 23 | 0.080 | Z_1=291.67 (p=0.777) |

## Housing + GDP per Capita Control (Corrected d_rhpi)

| Model | old_dep | p | youth_dep | p | R² | N |
|---|---|---|---|---|---|---|
| GDP/cap A: age ratios baseline | 78.1 | 0.390 | 63.1 | 0.535 | 0.063 | 541 |
| GDP/cap B: age ratios + log_gdppc | -29.3 | 0.752 | -44.6 | 0.669 | 0.104 | 466 |

**Verdict**: old_dep p-value: 0.390 → 0.752
